In its simplest design, a lidar is an optical device including a laser source, which emits a pulsed laser beam along an axis of sight, also called pointing direction, and a detection system that measures the reciprocating propagation time of the pulsed laser beam between the laser source and the target, the laser beam being reflected or backscattered by the target in the pointing direction and in the reverse direction of the incident laser beam. A lidar hence allows to measure the distance to a target.
There exist navigation and pointing systems integrating both a Lidar and a navigation unit, which indicates the geographic position and orientation of the system, to allow localising a target in space. In particular, navigation and pointing systems are known, in which a lidar is combined to an inertial navigation unit (INS, for Inertial Navigation System), as described for example in the article “Simultaneous Calibration of ALS Systems and Alignment of Multiview LiDAR Scans of Urban Areas”, M. Hebel and U. Stilla in IEEE Transactions on Geoscience and Remote Sensing, vol. 50, n° 8, June 2012.
The article “Tight Coupling of Laser Scanner and Inertial Measurements for a Fully Autonomous Relative Navigation Solution” A. Soloviev, D. Bates and F. van Graas in Navigation: Journal of the Institute of Navigation, vol. 54, n° 3, autumn 2007, aims to obtain an autonomous 2D relative positioning system.
In these navigation and pointing systems, there exist different types of lidar according to the means used to orient the pointing direction of the laser beam in space:                a 2D Lidar combines a lidar with a one-degree-of-freedom opto-mechanical system, such as for example a mirror rotating about an axis orthogonal to the axis of sight of the laser, adapted to vary the orientation of the laser beam in a plane of space (i.e. in 2D) and acquire in return measurements along a line (for example by projection onto a plane). Herein, each thus-acquired line is called a scan line or sweep line;        a 3D Lidar combines a Lidar with a two-degree-of-freedom opto-mechanical system, adapted to vary the orientation of the laser beam in all the directions of space (i.e. in 3D) and acquire in return measurements coming from any point in space. For example, a 3D Lidar may be consisted of a 2D Lidar mounted on a rotating table, allowing rotational movements about an axis orthogonal to that of the 2D-scan mirror.        
A system integrating a 2D-lidar or a 3D-lidar with a positioning system and an orientation system is called a “scanner laser”.
FIG. 1 shows an example of navigation and pointing system 10 comprising an inertial navigation unit 11 and a lidar 12 mechanically connected to each other by a rigid element 13, so that the INS and the lidar are integral with each other. The lidar 12 includes a laser source and a backscattered-beam detection system. The lidar 12 also includes a planar mirror 15 mounted mobile in rotation about an axis of rotation 16. For example, the normal to the plane of the mirror 15 is inclined at 45 degrees with respect to the direction of emission of the laser beam, which is preferably coaxial to the axis of rotation 16. By rotation 26 of the mirror 15 about the axis of rotation 16, the pointing direction 17 of the laser beam scans a plane 27, herein called scan plane. A two-dimensional lidar (2D lidar) is hence obtained, which allows to measure the distance of a target located in the scan plane 27. Knowing the pointing direction 17 in the reference system of the INS, it is then possible to provide the indications of position and orientation of the target with respect to a global reference system.
Depending on the devices, the rotation of the mirror 15 about the axis of rotation 16 may be either continuous, and always in the same direction, or oscillating, the mirror 15 performing reciprocal movements between two stops.
The navigation and pointing system 10 is for example mounted on a platform 14 rotationally mobile about an axis transverse to the axis of rotation 16 of the mirror 15. A rotation of the platform 14 causes the rotation of the whole system 10 and thus the rotation of the scan plane 27. A 3D lidar is hence obtained, which allows to measure the distance of a target in any pointing direction 17 in the three-dimensional space (3D lidar). So as to be able to geo-reference the LiDAR points, it is required to couple the lidar with other systems allowing to know the position and the orientation of the LiDAR.
The position and orientation are generally provided by a positioning system (denoted SP), such as a system combining a GPS localisation system and an inertial navigation unit {GPS+INS} or a GPS localisation system and a heading and vertical unit {GPS+AHRS}, for Attitude and Heading Reference System, or other. Hereinafter, it is meant by positioning system any system adapted to provide its position and orientation in a global reference system without making a distinction between the different possible sub-systems.
An AHRS unit (Attitude Heading Reference System) or an INS unit (Inertial Navigation System) are systems providing their orientation in a global reference system, such as the ECEF reference system. It then remains to know the relative orientation of the LiDAR with respect to the positioning and orientation system that is mechanically attached thereto.
Hereinafter, it is means by “LiDAR system” a system that combines a sighting instrument (the LiDAR), a positioning system and an orientation system. Such a lidar system hence provides measurements of position, orientation and sight.
By way of illustrative and non-limitative example, hereinafter, a system providing the orientation is illustrated by an INS.
A reference system 21 linked to the INS, hereinafter called INS reference system, is defined by a centre OSNI and three axes XSNI, YSNI and ZSNI (hereinafter, INS is referred to as SNI in the formulas and in the Figures). By convention, XSNI points forwards, YSNI points towards the right, and ZSNI points downwards. The navigation unit 11 allows at each instant to determine the position and orientation of the INS reference system with respect to a geographic reference system, or global reference system, for example the ECEF (Earth centred, Earth fixed) reference system defined by a geographic centre OECEF and three geographic axes XECEF, YECEF and ZECEF. The centre of the ECEF reference system is the centre of the Earth. The axes XECEF and YECEF are in the equatorial plane, XECEF points towards the Greenwich meridian and YECEF points towards 90 deg. East. Finally, ZECEF points towards the pole. The ECEF reference system is a global reference system, its centre is fixed.
A reference system 22 proper to the pointing system, herein called lidar reference system is defined by a centre Olidar and three axes Xlidar, Ylidar and Zlidar. The LiDAR considered herein is a 2D LiDAR. By convention, the axis Ylidar is the axis of rotation 16 of the mirror 15 and points towards the interface of the LiDAR that is considered as being the front of the LiDAR. Therefore, the LiDAR scans the plane (Xlidar, Zlidar), where Xlidar points towards the right of the LiDAR and Zlidar points towards the top. The plane (Xlidar, Zlidar) is also denoted scan plane 27 of the pointing direction 17 of the laser beam.
FIG. 2 schematically shows the INS reference system 21 and the lidar reference system 22 of the system of FIG. 1, with respect to the geographic reference system 20. The distance between the centre OSNI of the INS reference system and the centre Olidar of the lidar reference system is commonly called lever arm. By construction, herein, the axis XSNI of the INS reference system 21 is almost parallel to the axis Ylidar of the lidar reference system 22, the axis YSNI of the INS reference system 21 is almost parallel to the axis Xlidar of the lidar reference system 22, and the axis ZSNI of the INS reference system 21 is almost parallel and opposite to the axis Zlidar of the lidar reference system 22. Herein, almost parallel means aligned to within ±5 deg., or even to within better than 1 degree.
A rotation matrix comprising three Euler angles is defined to switch from the INS reference system to the lidar reference system. By construction, theses rotation angles are generally known to within better than a few degrees, or even to within a few tenth of degrees.
However, given that the lidar measures distances from a few meters to several hundreds of meters, an error in the angular orientation of the pointing direction may translate into a positioning error, which is not a constant bias error but an error varying according to the distance of the target.
It is therefore necessary to define a calibration method to determine the misalignment angles between the INS reference system and the lidar reference system. Let's denote misalignment angles (boresight error) the angles corresponding to the angular errors between the estimated reference system of the INS and the reference system 21 attached to the INS.
FIG. 3 schematically shows the change of reference system to switch from the reference system 21 proper to the INS to an estimated reference system 31.
FIG. 3 illustrates the three misalignment Euler angles (Φ, θ, ψ) that are desired to be calibrated. The misalignment angle ψ represents an angle of rotation about the axis ZSNI to switch from the reference system (XSNI, YSNI) to a reference system (X′SNI, Y′SNI). The misalignment angle θ represents an angle of rotation about the axis Y′SNI to switch from the reference system (X′SNI, ZSNI) to a reference system (X″SNI, Z″SNI), the axis Y′SNI being merged with the axis Y″SNI. The misalignment angle Φ represents an angle of rotation about the axis X″SNI to switch from the reference system (Y″SNI, Z″SNI) to the estimated reference system 31.
During the installation of the lidar system, the relative orientation of the two devices is known to within a few degrees. This relative orientation is expresses by the reference-system change matrix CLiDARS{circumflex over (N)}I.
The object of the calibration of the misalignment angles is to determine accurately the three misalignment Euler angles (Φ, θ, ψ) represented in FIG. 3.
This problem of calibration of the misalignment angles has already been tackled, in particular in aerial lidar (airborne lidar) applications in which a lidar system is taken on board an aircraft so as to scan or sweep the surface of the ground or of the building roofs during a displacement of the aircraft. In these applications of aerial lidar, the error on the misalignment angles is particularly critical. Indeed, the aerial lidars scan distances of several hundreds of meters. Now, the greater the pointing distance, the more the error on the position of the points measured by the lidar system is high, and thus easily observable.
The publication K. Kris Morin, Naser El-Sheimy, 2002, “Post-mission adjustment methods of airborne laser scanning data” In FIG. XXII International Congress, Washington, D.C. USA discloses the impact of the misalignment angle errors on the positioning of the points measured by an aerial lidar, and explains different methods of calibration. Two categories of calibration methods can be distinguished: on the one hand, the methods controlled by the data (Data-driven), and on the other hand the methods controlled by the system (System-driven).
A first data-driven calibration method consists in adjusting manually different acquisitions of lines or images by scanning the laser beam until the result is visually satisfying. This method is absolutely not mathematically rigorous and does not provide a statistical measurement about the quality of calibration.
Another data-driven calibration method is described in the publication Chao Gao, Spletzer, J. R., “On-line calibration of multiple lidars on a mobile vehicle platform”, Robotics and Automation (ICRA), 2010 IEEE International Conference, vol., no., pp. 279, 284, 3-7 May 2010. According to this publication, remarkable points, such as lines or contours, are identified in different images produced by the scanning (or scan) of a same zone. These remarkable points are then used to calculate the rotation matrix R and the translation vector T minimizing the deviation between these points {circumflex over (x)}LiDARecef. After correction, the points XLiDARecef are obtained:XLiDARecef=R·{circumflex over (X)}LiDARecef+T 
The data-driven methods are not based on any model and do not require collecting the position data of the GPS of the vehicle on board which the system is taken or the attitude data of the INS but only the lidar points. At first sight simple, these methods are not so in reality.
Indeed, the selection of remarkable points is not trivial because, even with a high-density acquisition of points, it is difficult to select accurately the same points in several scans, all the more since these points are noisy. This selection of points is not automatic, it takes a lot of time and the result of the calibration highly depends on the user.
Besides, as the data-driven methods are not based on a rigorous error model, they do not provide statistical measurement tools allowing to judge the quality of the adjustment.
The system-driven calibration methods are based on an error model, as disclosed, for example, in the publications Skaloud, J., Litchi, D., 2006, “Rigorous approach to boresight self-calibration in airborne laser scanning”, ISPRS Journal of Photogrammetry & Remote Sensing 61, 47-59 and Skaloud, J., Schaer, P., “Towards automated lidar boresight self-calibration”, in Proc. 5th International Symposium on Mobile Mapping Technology, Padua, Italy, 6 p, May 2007. This error model allows identifying systematic errors, including in particular the misalignment error between the lidar and the navigation unit. Therefore, a same operation of selection of remarkable points as above is performed, but the estimation of the misalignment angles requires the use of an error model.
A model of error of the following type is then used:XLiDARecef=XSPecef+CnecefCSNIn(b+(CS{circumflex over (N)}ISNICLiDARS{circumflex over (N)}I)XLiDARLiDAR)where ecef (earth centred earth fixed) denotes a geocentric and geostationary reference system;
CAB: represents generally a transition matrix from a reference system A to a reference system B;
Xαβ: represents generally a position of the device α in the reference system β;
b: represents the lever arm between the lidar and the positioning system.
The error model may also take into account other error parameters such as the lever arm errors, the bias on the angles of the INS, the bias on the distance measurement by the lidar . . . .
However, these methods of calibration require the intervention of a user to select remarkable points in the different scans.
The publication Skaloud, J., Schaer, P., “Towards automated lidar boresight self-calibration”, in Proc. 5th International Symposium on Mobile Mapping Technology, Padua, Italy, 6 p, May 2007 proposes to automatize the process of calibration of an aerial lidar system, by selecting a set of points belonging to a same surface, for example a roof, instead of comparing remarkable points two by two.
This approach allows the automation of the calibration algorithm. It is indeed easier to put in place processes of automatic detection/extraction of planes and of identification of common planes between different scans. This method gives satisfying results in aerial lidar because the distance to the targets is great and thus makes the error easily observable.
In the so-called terrestrial lidar systems, a lidar system is taken on board a terrestrial vehicle, for example on the roof of a car, and the laser beam scans the fronts of the buildings during displacements of the vehicle along a street, for example.
The conventional methods of calibration of terrestrial-lidar navigation and pointing systems are very widely inspired by the aerial lidar calibration approach, which seems to give good results.
Therefore, the publication Rieger, P., Studnicka, N., Pfennigbauer, M., Zach, G., “Boresight alignment method for mobile laser scanning systems”, Journal of Applied Geodesy. Volume 4, Issue 1, Pages 13-21 describes the calibration of a terrestrial lidar system by dynamically scanning a plane, during a displacement of the system in one direction and in the other one, and by varying the heading angle of the lidar according to four positions. This calibration requires at the minimum a total of 8 scans, each orientation having to be repeated at least two times.
The process being performed dynamically, the points have to be expressed in a global reference system (ex: ECEF). Once the points expressed in the global reference system, an algorithm detects the common planes formed by the lidar points between the different scans and estimates the misalignment angles by adjusting these planes of the different scans relative to each other.
However, the performance of such terrestrial lidar calibration is lesser than with an aerial lidar. Firstly, the pointing distances are far smaller (of the order of 10 m), which makes the error about the position of the lidar points far less easily observable. Moreover, it is not easy to vary enough the pointing distance to bring out the misalignment error. Further, the calibration process being performed dynamically, it is necessary to use a positioning system providing the position of the vehicle in real time. Now, during the terrestrial displacements, the GPS signal may be masked or affected by multipath propagations, which is less frequent in the aerial case. On the other hand, in terrestrial lidar, the diversity of orientation of the planes is lesser: there are mainly horizontal and vertical planes, whereas in aerial lidar, the building roofs offer generally a very varied range of orientations, allowing to reduce the correlation between the different misalignment angles. Finally, this method reveals to be sensitive to the bias on the angles given by the navigation unit, so that the misalignment angle values derived from this calibration are generally biased.
To sum up, the method of calibration of the misalignment angles are sensitive to different sources of errors: human errors, during the choice of the remarkable points, GPS errors, during the displacement of the system during calibration, and INS bias errors. Moreover, these calibration methods are time consuming.
There thus exists a need for a method of calibration of the misalignment angles that is both easy and fast to implement and preferably automatic. Another object of the invention is to provide a calibration method that is immune to the GPS errors. Another object of the invention is to provide a calibration method that is robust to lever arms. Still another object of the invention is to provide a calibration method that is insensitive to the INS biases so as to determine non-biased misalignment angles.